Function modelling using secondary data from E-STAT

 

Linear graph
Linear

Logistic graph
Logistic
Quadratic graph
Quadratic

Cubic graph
Cubic
Exponential graph
Exponential

Combined graph
Combined
Sinusoidal graph
Sinusoidal









In the real world, graphs related to human population or socioeconomic statistics rarely approximate any mathematical functions other than linear functions. However, there are some occasions where the underlying conditions lead to trends that closely approximate quadratic, exponential, sinusoidal and logistic functions or combinations of these functions.

Provided below are examples where real world data from Statistics Canada surveys can be approximated by function models. All data are extracted from E-STAT, a database available to educational institutions.

Note: You must use this information for educational purposes only.


Linear

Linear graph Click on graph to see more examples.

Data links for linear functions
Topic Years Table number Vector number
Total population 1971 to 2005 051-0001 v466668
Median age 1971 to 2005 051-0001 v466689
Revenue of fitness centres 2000 to 2004 361-0002 v1885072
Energy use by the business sector 1993 to 2000 153-0032 v29505744
Total pregnancies 1992 to 2000 106-9002 v14225258
Enterprises with a website 2000 to 2005 358-0008 v2651352
Life expectancy 1979 to 1999 102-0025 v5939197
Bottled water 1995 to 2001 002-0011 v783736
Lung cancer incidence (females) 1976 to 2004 103-0204 v41338730
Military personnel **Piecewise Linear** 1969 to 1998 183-0004 v130106

 

Quadratic

Quadratic graph Click on graph to see more examples.

Data links for quadratic functions
Topic Years Table number Vector number

Canadian births
**Convert to "Annual (sum)" under Manipulate data**

1948 to 1968 053-0001 v62
Number of males registered in apprenticeship programs 1991 to 2001 477-0051 v21691205
Lung cancer incidence (males) 1976 to 2000 103-0204 v41338718
Birth rate for women 40 years and over 1974 to 1999 106-9002 v14225341
Number of homicides by shooting 1978 to 1982 253-0002 v1489239

 

Exponential

Exponential graph Click on graph to see more examples.

Data links for exponential functions
Topic Years Table number Vector number
Federal debt 1955 to 1997 385-0010 v151537
Consumer price index 1951 to 2005 326-0002 v737344
Farm value of potatoes 1908 to 2004 001-0014 v47184
Infant mortality rate 1979 to 2005 102-0030 v5939543
Households with air conditioning 1999 to 2006 203-0020 v28469581
Urban population 1871 to 1971 075-0010 v742085

 

Sinusoidal

Sinusoidal graph Click on graph to see more examples.

Data links for sinusoidal functions
Topic Years Table number Vector number
Population aged 20-24 1971 to 2005 051-0001 v466758
Employment in the public sector
**Convert to "Annual (average)" under Manipulate data**
1981 to 2005 183-0002 v135015
Production of beer 2000 to 2003 303-0019 v1552
Imports of fresh fruits and berries 2000 to 2004 226-0002 v212580
Induced abortions for women under 20 years of age 1974 to 2003 106-9034 v31232487
International travellers to Canada (inbound) 1999 to 2008 387-0004 v81688
Employment rate 2002 to 2008 282-0001 v2091219

 

Logistic

Logistic graph Click on graph to enlarge.

Data links for logistic functions
Topic Years Table number Vector number
Cable television industry revenues 1976 to 2000 353-0001 v81330
Movie theatre ticket prices 1996 to 2005 501-0010 v26563414

 

Cubic

Cubic graph Click on graph to enlarge.

Data links for cubic functions
Topic Years Table number Vector number
Consumer price index – gasoline 1978 to 2008 326-0021 v41693434
Gross domestic product Q1-1970 to Q1-1978
Q1-1987 to Q4-1994
Q2-1999 to Q2-2003
380-0001 v498074
Labour force participation rate 1976 to 2005 282-0002 v2461247

 

Combined

Combined graph Click on graph to see more examples.

Data links for combined functions
Topic Years Table number Vector number
Canadian births
** Quadratic + Sinusoidal **
1955 to 1965 053-0001 v62
International travellers to Canada (inbound)
** Linear + Sinusoidal **
1999 to 2007 387-0004 v81688
Imports of fresh fruits and berries
** Linear + Sinusoidal **
1980 to 2004 226-0002 v212580
Employment rate
** Linear + Sinusoidal **
1993 to 2008 282-0001 v2091219
Urban and rural population
** Linear + Exponential **
1871 to 1971 075-0010 v742084

 

Extracting data from E-STAT

  1. You have two options:
  2. The next steps differ depending on your selection in #1:
  3. On the Output specification page, select the type of graph or table you wish to have displayed and then click on the Retrieve now button. Ensure that the start and end dates for the dataset are correct.

Suggestions for classroom use

  1. Have students research the reasons (historical, social, economic, etc.) why certain data follow certain patterns. 
    Suggestions:
  2. Have students import the data into a data analysis program and fit a function to the data by altering variable values.
  3. As a summative assessment of your course or unit on mathematical functions, give the students one of the real-world datasets above. Ask them to demonstrate their understanding of the course or unit by preparing a written analysis of this dataset. Evaluate the students' mathematical analysis and communication skills.